Skip to content
Rashevsky's Arithmetic cover
Available Now

Rashevsky's Arithmetic

by K. N. Rashevsky

Translated by Valery Manokhin, PhD

A complete course in arithmetic in nine sections, in first faithful English translation from the original Russian edition. The four operations on whole numbers with the written methods set out in full; named and metric quantities; areas and volumes worked from drawings; tests for divisibility, primes, greatest common divisor and least common multiple; common and decimal fractions, including repeating decimals; ratio, proportion and proportional division; percentage and mixing problems; and plans, diagrams and graphs. Long divisions and column multiplications are printed digit under digit, so the reasoning stays visible on the page.

9 chapters · 95 pages

Where this fits in school — US, UK and Canada ↓ Adults and self-learners welcome — great mathematics has no age limit.

$39.95 Buy Now — Paperback Amazon Paperback

Where this fits in school

Full curriculum table — every book by school year →
United States5–8Grade 6–7 math → Pre-Algebra; also a complete adult refresher
United KingdomYears 6–9KS2 into KS3 · percentage work reaches GCSE Foundation
CanadaOntario 5–8BC Math 5–8 · QC Elementary 5 – Secondary II

Not covered in this book

negative numbers · statistics and data handling · probability

Source these strands elsewhere. They are missing from the book, not from this description.

How this book fits

See the whole sequence →

Covers much of the same ground

  • Kiselev's Systematic Arithmetic$49.95

    The systematic course runs to 264 numbered articles over 207 pages and treats divisibility, ratio and proportion far more fully. This book covers the same ground in 95 pages and adds plans, diagrams and graphs, which the systematic course does not treat.

  • Kiselev's Arithmetic$44.95

    Kiselev's is the school course, six sections and 214 numbered articles, written for a child meeting arithmetic for the first time. This one is nine sections in 95 pages, written for a reader who wants the whole subject back in order, and it ends with plans, diagrams and graphs, which Kiselev's does not treat.

These overlap heavily. Each note says what that book has which this one does not — the differences are what decide between them.

What comes next

Table of contents

166 section headings — the printed contents page in full.

Translator's Preface

I. ELEMENTARY CONCEPTS3 sections
  1. 1. Definitions
  2. 2. Numeration table
  3. 3. Roman numeration
II. ARITHMETICAL OPERATIONS44 sections
  1. 4. Definitions
  2. ADDITION
  3. 5. Definitions
  4. 6. Property of the sum
  5. 7. Addition table
  6. 8. Placement of names
  7. 9. Uses of addition
  8. SUBTRACTION
  9. 10. Definitions
  10. 11. Uses of subtraction
  11. 12. Addition and subtraction
  12. 13. Placement of names
  13. 14. Examples of subtraction
  14. MULTIPLICATION
  15. 15. Definitions
  16. 16. Main property of the product
  17. 17. Special cases of multiplication
  18. 18. Multiplication table
  19. 19. Rule
  20. 20. Rule
  21. 21. Definitions
  22. 22. Use of multiplication
  23. 23.
  24. 24. Placement of names
  25. DIVISION
  26. 25. Definitions
  27. 26. Division with a remainder
  28. 27. Special cases of division
  29. 28.
  30. 29. Uses of division
  31. 30. Placement of names
  32. 31.
  33. CHECKING THE OPERATIONS
  34. 32.
  35. ARITHMETICAL EXPRESSIONS AND PARENTHESES
  36. 33.
  37. CHANGES IN THE SUM, DIFFERENCE, PRODUCT, AND QUOTIENT
  38. 34. Change in the sum
  39. 35. Change in the difference
  40. 36. Change in the product
  41. 37. Change in the quotient (division without a remainder)
  42. PROPERTIES OF THE OPERATIONS
  43. 38.
  44. 39. Special cases of the operations
III. NAMED NUMBERS21 sections
  1. 40. Definitions
  2. METRIC MEASURES
  3. 41. Measures of weight
  4. 42. Measures of length
  5. 43. Measures of area, or square measures
  6. 44. Measures of volume, or cubic measures
  7. 45. Measures of dry goods and liquids
  8. 46. Measures of paper
  9. 47. Money
  10. 48. Measures of time
  11. 49. The calendar
  12. 50. Symbols for metric measures
  13. 51. Converting larger measures into smaller ones
  14. 52. Converting smaller measures into larger ones
  15. 53. Addition and subtraction of compound named numbers
  16. 54. Problems in calculating time
  17. 55. Multiplication of compound named numbers
  18. 56. Division of compound named numbers
  19. DETERMINATION OF AREAS AND VOLUMES
  20. 57.
  21. 58.
IV. TESTS FOR DIVISIBILITY2 sections
  1. 59. Definition
  2. 60.
V. COMMON FRACTIONS, THEIR TRANSFORMATIONS, AND OPERATIONS ON THEM30 sections
  1. 61.
  2. 62. Rule
  3. 63. Rule
  4. 64. Comparing fractions
  5. 65. Rule
  6. 66. Main property of a fraction
  7. 67. Reducing fractions
  8. 68. Expressing fractions in other parts
  9. 69.
  10. 70. Remark
  11. 71. Example 1
  12. 72. Addition of fractions
  13. 73. Rule
  14. 74. Subtraction of fractions
  15. 75. Multiplication of fractions
  16. 76. Rule
  17. 77. Cancellation when multiplying fractions
  18. 78.
  19. 79.
  20. 80.
  21. 81. Division of fractions
  22. 82.
  23. 83. Definition
  24. 84. General rule of division
  25. 85.
  26. FINDING A PART OF A NUMBER AND A NUMBER FROM ITS PART
  27. 86.
  28. OPERATIONS WITH FRACTIONAL NAMED NUMBERS
  29. 87.
  30. 88. Remark
VI. DECIMAL FRACTIONS27 sections
  1. 89. Definition
  2. 90. Reading decimal fractions
  3. 91. Rule
  4. 92. Main property of a decimal fraction
  5. 93. Rule
  6. 94. Rule
  7. 95. Comparing decimal fractions
  8. 96. Rule
  9. 97. Addition and subtraction of decimal fractions
  10. 98. Multiplication of decimal fractions
  11. 99. Division of decimal fractions
  12. 100. Approximate quotient
  13. 101. Rule
  14. APPROXIMATE CALCULATIONS
  15. 102. Addition
  16. 103. Abbreviated multiplication
  17. 104. Abbreviated division
  18. 105. Converting common fractions to decimals
  19. 106. Definition
  20. 107. Theorem
  21. METRIC SYSTEM OF MEASUREMENT
  22. 108.
  23. 109.
  24. 110. Metric monetary units
  25. 111. Use of tables
  26. 112. Tables for converting Russian measures to metric measures
  27. 113. Advantages of the metric system
VII. DIVISORS AND MULTIPLES8 sections
  1. 114. Absolutely prime and composite numbers
  2. 115. Eratosthenes' sieve
  3. 116. Factoring numbers into prime factors
  4. 117. Greatest common divisor
  5. 118. Rule
  6. 119. Rule
  7. 120. Relatively prime numbers
  8. 121. Rule
VIII. PROPORTION. PROBLEMS ON PROPORTIONAL QUANTITIES23 sections
  1. 122. Ratio and proportion
  2. 123. Definition
  3. 124. Fundamental property of a proportion
  4. 125.
  5. 126. Definition
  6. 127. Proportional quantities
  7. PERCENTAGE CALCULATIONS
  8. 128. Definition
  9. 129. Definitions
  10. 130. Problem 1
  11. DISCOUNTING BILLS
  12. 131.
  13. 132. Problem
  14. PROPORTIONAL DIVISION
  15. 133. Problem
  16. 134. Problem
  17. 135. Problem
  18. 136. Problem
  19. MIXING PROBLEMS
  20. 137. Definition
  21. 138. Problem
  22. 139. Problem
  23. 140. Problem
IX. DRAWING PLANS, DIAGRAMS, AND GRAPHS8 sections
  1. 141. Plan
  2. 142. Diagrams
  3. 143. Percentage diagrams
  4. 144. Circular diagram
  5. GRAPHICAL METHOD FOR SOLVING PROBLEMS
  6. 145. Function
  7. 146. Graph
  8. 147. Problem 1

TABLE OF PRIME NUMBERS

Search the contents of every book →

Formats and editions

FormatPriceISBN-13WhereBuy
Paperback$39.95978-1-919012-86-5AmazonBuy →

Prices are the publisher list prices. Amazon sets the final price in each store.

Product details

Publisher
Northern Star Academic Press
Language
English
Translator
Valery Manokhin, PhD
Print length
95 pages
First published
2026-09-19

Published by Northern Star Academic Press · First faithful English translation from the original Russian edition

Browse the full Russian Math Classics series on Amazon →

More in This Series

Rachinsky's 1001 Problems cover
Available Now

Rachinsky's 1001 Problems

by S. A. Rachinsky

US grades 4–8 · UK Years 5–9

1,001 carefully selected problems from the village schoolteacher whose students were depicted in Bogdanov-Belsky's famous 1895 painting "Mental Arithmetic."

$39.95 Learn More →
Perelman's Entertaining Arithmetic cover
Available Now

Perelman's Entertaining Arithmetic

by Ya. I. Perelman

US grades 4+ · UK Year 5+

The classic of Russian popular mathematics. Puzzles, riddles, and curiosities that make arithmetic genuinely entertaining.

$34.95 Learn More →
Markov: Probabilities cover
Available Now

Markov: Probabilities

by Andrei A. Markov

US grades 12 and university · UK Year 13 and university

The foundational 1900 work on probability theory by the mathematician who gave us Markov chains. A modern annotated English translation.

$59.95 Learn More →

Get Notified When New Translations Launch

New translations are announced to the newsletter first — with sample chapters. Join math educators and parents who follow this project.

New translation announcements, sample chapters, and teaching notes. No spam.

Also by Valery Manokhin — Machine Learning & Forecasting books at

valeriy.ai · Substack Newsletter